Thursday, June 9, 2016
09:45 - 10:00
Opening
10:00 - 10:45
Bruno Franchi (Alma Mater Studiorum Università di Bologna)
Gagliardo-Nirenberg inequalities for differential forms in Heisenberg groups download abstract
10:45 - 11:15
Coffee Break
11:15 - 12:00
Bernard Dacorogna (École polytechnique fédérale de Lausanne)
Symplectic decomposition, Darboux theorem and ellipticity. download abstract
12:10 - 12:55
Sandro Salsa (Politecnico di Milano)
On free boundary problems with distributed sources. view abstract Sandro Salsa
On free boundary problems with distributed sources.

We describe some recent results obtained jointly with D. De Silva and F. Ferrari on existence and regularity for free boundary roblem governed by elliptic equations with distributed sources. We also shall point out some open problems in these area.
15:00 - 15:45
Ireneo Peral (Universidad Autónoma de Madrid)
The effect of the Hardy potential in some Calderón-Zygmund properties for the fractional Laplacian. download abstract
15:55 - 16:40
Roberto Monti (Università degli studi di Padova)
Recent results on isoperimetric problems in Heisenberg type spaces. view abstract Roberto Monti
Recent results on isoperimetric problems in Heisenberg type spaces.

We present some recent results on the isoperimetric problem in the Heisenberg group, in Grushin-type spaces and in H-type groups. In particular, we shall present a quantitative version of the isoperimetric inequality in the Heisenberg group in a cylindrical setting.

The results are a joint work with G. P. Leonardi and V. Franceschi.
16:40 - 17:05
Coffee Break
17:05 - 17:50
Giuseppe Di Fazio (Università degli studi di Catania)
Strong $A_\infty$ weights and quasilinear degenerate elliptic equations download abstract
18:00 - 18:45
Vincenzo Vespri (Università degli studi di Firenze)
Harnack estimates at large for quasilinear parabolic equations. view abstract Vincenzo Vespri
Harnack estimates at large for quasilinear parabolic equations.

We prove Harnack estimates for of a class quasilinear parabolic equations whose prototypes are p-Laplacean equations. In the linear case, similar estimates (even if not sharp) were proved by Moser for linear operators thanks to the Harnack chain technique. Sharp estimates in the linear case are due to Fabes, Stroock and Coulhon by using Nash estimate, The last approach cannot be generalised to the quasilinear case. In this talk we describe how to get sharp estimates in the quasilinear cases too via a direct approach based on DeGiorgi techniques.
20:30
Social Dinner at Ristorante Belle Arti
Friday, June 10, 2016
09:15 - 10:00
Italo Capuzzo Dolcetta (Sapienza Università di Roma)
Some new results about the weak maximum principle. view abstract Italo Capuzzo Dolcetta
Some new results about the weak maximum principle.

A few new results about the validity of the weak maximum principle operators from different viewpoints will be discussed in the talk:
- fully nonlinear degenerate elliptic operators
- connections with the positivity of a generalized principal eigenvalue
- one directional ellipticity
- special unbounded domains
I will report in particular on recent research in [1], [2], [3]:
[1] H. Berestycki, A. Porretta, L. Rossi, ICD, Maximum Principle and generalized principal eigenvalue for degenerate elliptic operators, JMPA 2014
[2] I. Birindelli, F. Camilli, ICD, On the approximation of the principal eigenvalue for a class of nonlinear elliptic operators, Communications in Math. Sciences 2016
[3] ICD, A. Vitolo, The weak Maximum Principle for degenerate elliptic operators in unbounded domains, submitted 2016
10:10 - 10:55
Sorin Dragomir (Università degli studi della Basilicata)
Boundary Behavior of Bergman-harmonic Maps. download abstract
10:55 - 11:25
Coffee Break
11:25 - 12:10
Martino Bardi (Università degli studi di Padova)
Liouville properties of fully nonlinear elliptic operators and some applications. view abstract Martino Bardi
Liouville properties of fully nonlinear elliptic operators and some applications.

I will present a joint paper with Annalisa Cesaroni (Padova). We prove some Liouville properties for sub- and supersolutions of fully nonlinear degenerate elliptic equations in the whole space. Our assumptions allow the coefficients of the first order terms to be large at infinity, provided they have an appropriate sign, as in Ornstein-Uhlenbeck operators. We give two applications. The first is a stabilization property for large times of solutions to fully nonlinear parabolic equations. The second is the solvability of an ergodic Hamilton-Jacobi-Bellman equation that identifies a unique critical value of the operator.
12:20 - 13:05
Zoltan Balogh (Universität Bern)
Geometric inequalities on Heisenberg groups download abstract
15:00 - 15:45
Enzo Mitidieri (Università degli studi di Trieste)
Some unexpected Liouville theorems for a semilinear biharmonic equation. download abstract
15:55 - 16:40
Ermanno Lanconelli (Alma Mater Studiorum Università di Bologna)
Measures with the mean value property for L-harmonic functions: an inverse problem download abstract